# No net generation or recombination of electrons is assumed

I am currently studying the textbook Physics of Photonic Devices, second edition, by Shun Lien Chuang. Section 2.1.1 Maxwell's Equations in MKS Units says the following:

The well-known Maxwell's equations in MKS (meter, kilogram, and second) units are written as $$\nabla \times \mathbf{E} = - \dfrac{\partial}{\partial{t}}\mathbf{B} \ \ \ \ \text{Faraday's law} \tag{2.1.1}$$ $$\nabla \times \mathbf{H} = \mathbf{J} + \dfrac{\partial{\mathbf{D}}}{\partial{t}} \ \ \ \ \text{Ampére's law} \tag{2.1.2}$$ $$\nabla \cdot \mathbf{D} = \rho \ \ \ \ \text{Gauss's law} \tag{2.1.3}$$ $$\nabla \cdot \mathbf{B} = 0 \ \ \ \ \text{Gauss's law} \tag{2.1.4}$$ where $$\mathbf{E}$$ is the electric field (V/m), $$\mathbf{H}$$ is the magnetic field (A/m), $$\mathbf{D}$$ is the electric displacement flux density (C/m$$^2$$), and $$\mathbf{B}$$ is the magnetic flux density (Vs/m$$^2$$ or Webers/m$$^2$$). The two source terms, the charge density $$\rho$$(C/m$$^3$$) and the current density $$\mathbf{J}$$(A/m$$^2$$), are related by the continuity equation $$\nabla \cdot \mathbf{J} + \dfrac{\partial}{\partial{t}}\rho = 0 \tag{2.1.5}$$ where no net generation or recombination of electrons is assumed.

where no net generation or recombination of electrons is assumed.

What does this mean in simpler terms? Why is this assumption necessary for $$\nabla \cdot \mathbf{J} + \dfrac{\partial}{\partial{t}}\rho = 0$$?

The number/concentration of electrons in a volume may be due to their flow into / out of the volume (electric current), or due to the electrons appearing/disappearing inside of it. In vacumm, the latter possibility can be usually safely ignored (although not in QFT), so we have the continuity equation: $$\nabla\cdot\mathbf{J}+\partial_t\rho=0\Leftrightarrow \int_S\mathbf{J}\cdot\mathbf{ds} + \partial Q=0,$$ where the second equation is just the integral form of the continuity equation: the total current flowing through the surface surrounding the volume is the change of the charge within.
If, however, the charge may appear/vanish within the volume – which is a real option in semiconductors' interaction with the electromagnetic field – then we need to augment the continuity equation with a source term: $$\nabla\cdot\mathbf{J}+\partial_t\rho=s(t)$$